Relativistic Law Of Reflection

[LightStorm]

Hi all. A 90 degree ray of light (from a star) hits a mirror (on the earth) that is slanted at 45 degrees. Then the ray goes to an eye piece.The angle made by the ray of light when it reaches the eye piece is 90 degrees. But as seen from the star frame, the 90 degree ray hits a contracted mirror (due to earth's motion and is no longer slanted at 45 degrees) and therefore the ray of light will miss the eye piece. What is the resolution to this problem?

[LightStorm]

On a moving mirror, according to relativistic law of reflection, the angle of reflection is not equal to the angle of incidence. Therefore, the angles can't be the same in both the frames. The star frame should see a different reflection than the earth frame. Meaning in one frame, the light misses the eye piece. Or the angle of reflection is the same in both the frames. But that contradicts relativistic law of reflection.

[ralfcis]

No such thing as length contraction.

[sluggo]

On a moving mirror, according to relativistic law of reflection, the angle of reflection is not equal to the angle of incidence. Therefore, the angles can't be the same in both the frames. The star frame should see a different reflection than the earth frame. Meaning in one frame, the light misses the eye piece. Or the angle of reflection is the same in both the frames. But that contradicts relativistic law of reflection.

The mirror gets thinner, but the angle remains constant.

[OceanBreeze]

The mirror gets thinner, but the angle remains constant.

 

No. The mirror thins in the x direction but the height in y direction remains constant, so the angle must change (it gets less with respect to y axis)

 

See this explanation here.

[ralfcis]

Which is what he said in his first post. This could be an interesting example to solve using time only as there's no such thing as length contraction. 

 

PS. Considering time only, this is the same as the moving light clock example. The angle of the light bouncing off the light clock mirrors gets smaller as the light clock's speed increases relative to a stationary observer. Like I said, there's no such thing as length contraction. As Einstein said a theory should be as simple as possible and he also said his theory depends on both time dilation and length contraction working together to guarantee the constancy of c from all perspectives. This is his explanation for the MMX and my explanation does not require length contraction. So then  his theory is not as simple as possible and therefore must go into the trash can of history by his own words.

Edited October 3, 2019 by ralfcis

[ralfcis]

Someone should ask me the question of why I'm such a failure in life when I'm just so damn smart.

[ralfcis]

Here's a video

 

https://www.youtube.com/watch?v=v8lzsYh3JRY&list=PLj6DWzIvBi4PFDXCCV1bNhVUgDLTwVbFc&index=14&t=0s

 

No mention of length contraction anywhere. Even the length the moving clock traverses is not length contracted simply because length contraction and time dilation do not work together simultaneously to keep c constant from all perspectives as Dildostein seemed to think.

 

To be fair, there's also no such thing as time dilation either. Time itself doesn't slow in this example, it's the velocity that causes a rate of time information delay to the observer. The rate of time itself is unaffected. 

Edited October 3, 2019 by ralfcis

[ralfcis]

You know, I've noticed that whatever thread I participate in on any forum I've been on (except the serious ones) the readership skyrockets. Hmmm. maybe I too am an narcissist and am just in it for the clicks.

[LightStorm]

No such thing as length contraction.

 

I think the same. Light reflects as if there were no contraction in either frame. Classical reflection in both frames.

[LightStorm]

The mirror gets thinner, but the angle remains constant.

 

The mirror remains unchanged. Classical reflection in both the frames is the right answer. Relativity agrees with the outcome that the reflections are classical, but in a roundabout way. Which is why the ray doesn't miss the eye piece in either frame.

Edited October 4, 2019 by LightStorm

[Vmedvil2]

The energy-mass of the star only effects the space in the region near the star as gravitational potential energy generates length contraction called curvature. secondly, the angles are not effected as it is bend toward the star as it moves away from the star in a straight line back toward the star. thirdly, frames do not matter in this situation as it is a photon and follows the light cone unless effected by gravity as light only has a constant velocity of C always as it does not have mass, Special Relativity has no control over photons as they follow the light cone, only general relativity, which the gravity if strong enough will bend the photon to a different angle but that is a gravitational effect, the angle due to gravity will be slightly and I mean slightly different from the 45 degree angled mirror because of gravity but not special relativity, this has nothing to do with frames it is a universal effect of gravitational curvature which is constant per unit mass. The light will miss the eye piece if not corrected for gravity of the earth as the gravity will change the direction in transit.

 

Edited October 4, 2019 by VictorMedvil

[ralfcis]

Your question is good because it highlights the thing most misinterpreted about relativity. If the light hits the eyepiece in any frame, it must hit the eyepiece from any perspective. Reality is not subjective and fractured into equally valid perspectives. The event is invariant but due to the lag or lead of moving clocks relative to other clocks, the timing of the event is affected by the perspective. There is no length contraction because if the angle of the mirror shrinks due to length contraction there is no reason to assume the angle of the light off the mirror doesn't also shrink due to time dilation. But that double shrinking doesn't happen because both are mathematically the same phenomenon. 

 

Victor, what are you posting? Completely irrelevant stuff.

[sluggo]

No. The mirror thins in the x direction but the height in y direction remains constant, so the angle must change (it gets less with respect to y axis)

 

See this explanation here.

Yes, the contraction occurs in the x axis, but a slice in that direction is affected to the same degree, from top of mirror to bottom.

If the mirror face was on a prism, then the contraction is proportional top to bottom, and the prism would be deformed.

[OceanBreeze]

Yes, the contraction occurs in the x axis, but a slice in that direction is affected to the same degree, from top of mirror to bottom.

If the mirror face was on a prism, then the contraction is proportional top to bottom, and the prism would be deformed.

 

Well, you do agree that the contraction is only along the x-axis, correct?

If so, you should be able to agree that the tilt angle must change.

Ly is the length along the y-axis, which does not change

Lx is the length along the x-axis, which changes to Lx’ as seen from the frame in relative motion

Tan Θ =  (the angle of tilt in the rest frame of the mirror with respect to the y axis)

Tan ϕ = Lx’/Ly (the change in the angle of tilt as seen from the frame in relative motion with respect to the y-axis)

 

It can be deduced that (Θ + ϕ)  is not equal to  Θ

 

If you still don’t agree just do a search of length contraction and angle rotation and you should come up with several explanations that may be more detailed and better than my own simplistic explanation.

 

Additionally, I believe the answer to the problem posed in the OP is just that aberration of light changes the angle of the incident light beam in a way to exactly compensate for the changed angle of mirror tilt. This should not be surprising since both phenomena are dependent on velocity, but I’m too lazy to post the math right now.

Edited October 4, 2019 by OceanBreeze
had some mistakes

[OceanBreeze]

Your question is good because it highlights the thing most misinterpreted about relativity. If the light hits the eyepiece in any frame, it must hit the eyepiece from any perspective. Reality is not subjective and fractured into equally valid perspectives. The event is invariant but due to the lag or lead of moving clocks relative to other clocks, the timing of the event is affected by the perspective. There is no length contraction because if the angle of the mirror shrinks due to length contraction there is no reason to assume the angle of the light off the mirror doesn't also shrink due to time dilation. But that double shrinking doesn't happen because both are mathematically the same phenomenon. 

 

Victor, what are you posting? Completely irrelevant stuff.

 

Your instincts are good even though you deny length contraction.

 

I somewhat agree with the bold font as you might see in my comment about aberration of light.

[Vmedvil2]

Your question is good because it highlights the thing most misinterpreted about relativity. If the light hits the eyepiece in any frame, it must hit the eyepiece from any perspective. Reality is not subjective and fractured into equally valid perspectives. The event is invariant but due to the lag or lead of moving clocks relative to other clocks, the timing of the event is affected by the perspective. There is no length contraction because if the angle of the mirror shrinks due to length contraction there is no reason to assume the angle of the light off the mirror doesn't also shrink due to time dilation. But that double shrinking doesn't happen because both are mathematically the same phenomenon. 

 

Victor, what are you posting? Completely irrelevant stuff.

Oh now I am just laughing to myself about how all of you claim to know what is happening yet none of you have considered the gravitational effects. Did I say something that was above your head? did you not understand that curvature via gravity would effect the travel path of the light.

Edited October 4, 2019 by VictorMedvil